156081

First I analyzed the 6 fractions and looked at which ones could add together to get a number close to one. After a few tries not working I then chose to add 5/8 and 4/15 which was equivalent to 107/120 as 120 is the least common multiple of the two denominators 15 and 8. I then found any other denominators that could multiply into 120 and the fractions were 3/5, 1/6 and 1/20. These fractions were equivalent to 72/120, 20/120 and 6/120. After adding all these numbers on in separate equations the closest answer was 127 after adding the 1/6 or 20/120. This is equivalent to 1.058, just .058 of the number 1.

This is as close as I could get to 1.